Abstract
Using polar conics of plane cubics we define a rational map \(\Psi_m: \mathcal{M}_6^b \rightarrow \mathcal{M}_D\) from the moduli space of stable binary sextics into the moduli space of Desargues configurations. We show that this map is the inverse of a birational map \(\Phi_s: \mathcal{M}_D \rightarrow \mathcal{M}_6^b\) defined via the von Staudt conic. In particular Ψm is a birational map.
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